| On von-Neumann Regular Rings and Left SF-Rings |
| Received:April 23, 2002 |
| Key Words:
regular ring strongly regular ring SF-ring generalized weak ideal.
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| Fund Project: |
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| Abstract: |
| A rings R is defined to be a left SF-ring if all simple left R -modules are flat. It is known that von Neumann regular rings are SF-rings. But the question whether a left SF-ring is necessarily regular remains open. In this paper, we study the regularity of left SF-rings which satisfy certain additional conditions. It is proved that R is strongly regular if R is a left SF-ring whose maximal left (right) ideals are generalized weak ideals. Furthermore, we generalize some results in [3]. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2004.04.014 |
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